Answer:
0.7325 to 5.6675 ug/dl
Step-by-step explanation:
The middle 90% will be 45% above the mean and 45% below the mean. This means
0.5-0.45 = 0.05 and
0.5+0.45 = 0.95
We use a z table. Look in the cells; find the values as close to 0.05 and 0.95 as we can get.
For 0.05, we have 0.0505 and 0.0495; since these are equidistant from 0.05, we use the value between them. 0.0505 is z=-1.64 and 0.0495 is z=1.65; this gives us z=-1.645.
For 0.95, we have 0.9495 and 0.9505; since these are equidistant from 0.95, we use the value between them. 0.9495 is z = 1.64 and 0.9505 is z=1.65; this gives us z = 1.645.
Now we use our z score formula,
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Our two z scores are 1.645 and -1.645; our mean, μ, is 3.2; and our standard deviation, σ, is 1.5:
[tex]1.645=\frac{X-3.2}{1.5}[/tex]
Multiply both sides by 1.5:
[tex]1.5(1.645)=\frac{X-3.2}{1.5}\times 1.5\\\\2.4675 = X-3.2[/tex]
Add 3.2 to each side:
2.4675+3.2 = X-3.2+3.2
5.6675 = X
[tex]-1.645=\frac{X-3.2}{1.5}[/tex]
Multiply both sides by 1.5:
[tex]1.5(-1.645)=\frac{X-3.2}{1.5}\times 1.5\\\\-2.4675=X-3.2[/tex]
Add 3.2 to each side:
-2.4675+3.2 = X-3.2+3.2
0.7325 = X
Our range is from 0.7325 to 5.6675.
Final answer:
The range of arsenic blood concentrations corresponding to the middle 90% of healthy adults is approximately 0.765 ug/dl to 4.035 ug/dl.
Explanation:
The middle 90% of a Normally distributed data set falls within approximately two standard deviations of the mean. In this case, the mean is 3.2 ug/dl and the standard deviation is 1.5. To find the range of arsenic blood concentrations corresponding to the middle 90% of healthy adults, we can calculate the upper and lower boundaries.
First, we need to find the Z-scores that correspond to the 5th and 95th percentiles. The Z-score formula is:
Z = (x - mu) / sigma
Applying the formula, we get:
Z_lower = (x_lower - 3.2) / 1.5 = -1.53
Z_upper = (x_upper - 3.2) / 1.5 = 1.53
Next, we need to find the corresponding x values. Rearranging the Z-score formula, we can solve for x:
x = Z * sigma + mu
Plugging in the Z scores, we have:
x_lower = -1.53 * 1.5 + 3.2 = 0.765
x_upper = 1.53 * 1.5 + 3.2 = 4.035
Therefore, the range of arsenic blood concentrations corresponding to the middle 90% of healthy adults is approximately 0.765 ug/dl to 4.035 ug/dl.
The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,500 per day. FSF supplies hot dogs to local restaurants at a steady rate of 260 per day. The cost to prepare the equipment for producing hot dogs is $66. Annual holding costs are 46 cents per hot dog. The factory operates 296 days a year. a. Find the optimal run size. (Do not round intermediate calculations. Round your answer to the nearest whole number.) Optimal run size b. Find the number of runs per year. (Round your answer to the nearest whole number.) Number of runs c. Find the length (in days) of a run. (Round your answer to the nearest whole number.) Run length (in days)
Answer:
a. 5218 hot dogs
b. 18 runs per year
c. 1 day per run
Step-by-step explanation:
(a) Let n represent the number of hotdogs in an optimal run. The number of runs needed in a year is ...
r = (260 hotdogs/day)·(365 days/year)/(n hotdogs/run) = 94900/n runs/year
The number of hotdogs in storage decreases from n at the end of a run to 0 just before a run. The decrease is linear, so the average number in storage is n/2.
We can go to the trouble to write the equation for total cost, then differentiate it to find the value of n at the minimum, or we can just jump to the solution. That solution is ...
holding cost = setup cost
(n/2)·0.46 = (94900/n)·66
n^2 = 94900·66·2/0.46 = 27,232,173.9
n ≈ 5218.446
The optimal number of hotdogs in a run is 5218.
___
(b) The number of runs needed per year is (from part (a)) ...
r = 94900/5218 ≈ 18.187
The number of runs per year is 18.
___
(c) The run lenght is 5218 hotdogs, and the run produces them at the rate of 5500 hotdogs/day, so the run length in days is ...
(5218 hotdogs)/(5500 hotdogs/day) = 0.9487 days
The run length is 1 day.
The number 400 is increased by 75%. The result is then decreased by 50%. What is the final number?
Answer:150
Step-by-step explanation:75 on 100 multiply by 400 u will get 300.then 50 on 100 multiply 300 .your answer is 150.check???
Answer:
150.
Step-by-step explanation:
(2Q) The graph of the logarithmic function y = loga(x) always passes through what point?
Answer:
(1,0)
Step-by-step explanation:
The given logarithmic function is
[tex]y=\log_ax[/tex]
When [tex]x=1[/tex], the logarithmic function becomes;
[tex]y=\log_a1[/tex]
[tex]\Rightarrow y=\log_aa^0[/tex]
[tex]\Rightarrow y=0(\log_aa)[/tex]
[tex]\Rightarrow y=0(1)[/tex]
[tex]\Rightarrow y=0[/tex]
Therefore the graph always passes through;
[tex](1,0)[/tex]
Answer:
option D
(1,0)
Step-by-step explanation:
Given in the question an expression
y = [tex]log_{a}x[/tex]
This function's graph will always pass through x-axis where y will always be 0
y = [tex]log_{a}x[/tex]
0 = [tex]log_{a}x[/tex]
This situation is only possible when x = 1
0 = [tex]log_{a}1[/tex]
Secondly, x can never be zero
As,
[tex]y = log_{a}0[/tex] is undefined
so this eliminate option (A) and (C)
etermine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 3 2 x − 2y = 4 x + 1 3 y = 2 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Answer:
(32/15, -2/5)
Step-by-step explanation:
(1) ³/₂x - 2y = 4
(2) x + ⅓y = 2
(3) 3x - 4y = 8 Multiplied (1) by 2
(4) 3x + y = 6 Multiplied (2) by 3
5y = -2 Subtracted (3) from (4)
(5) y = -⅖ Divided each side by 5
x + ⅓(-⅖) = 2 Substituted (5) into (2)
x - ²/₁₅ = 2
x = 2 + ²/₁₅ Added ²/₁₅ to each side
x = 32/15
The system of equations has only one solution: (32/15, -2/5).
4O POINTS AND BRAINLIEST!!!!!!!!!!!!
1. The value of y varies directly with x, and y = 12 when x = −6.
Find y when x = −4.
2. The value of y varies directly with x, and y = 3 when x = −6.
Find y when x = 1.
3. The value of y varies directly with x, and y = −12 when x = 6.
Find y when x = −4.
4. The value of y varies directly with x, and y = 3 when x = 1.
Find y when x = −5.
1. 8 (k=-2)
2. 8 (k=-0.5)
3. 8 (k=-2)
4. -15 (k=3)
This is literally 20 points of my grade pls help! very desperate.
Answer:
Step-by-step explanation:
see attached
A town uses positive numbers to track increases in population and negative numbers to track decreases in population. The population has decreased by 300300300 residents over the past 555 years. The same number of residents left each year. What was the change in the town's population each year?
Answer:
-60 people
Step-by-step explanation:
The change in population was -300 people.
The change in population was -300 people/5 yr or -60 people/yr.
dish television charges a one-time installation fee and a monthly service charge. The total cost is modeled by the equation y=120+75x.
The total cost is represented by:
The number of months is represented by:
The installation fee is:
the monthly charge is:
y = 120 + 75x
y is total charge
75x where 75 is monthly charge and x is number of months
120 is installation charges.
Dish television charges modeled by the equation represents,
a) The total cost is represented by variable y.b) The number of months is represented by is represented by variable x.c) The installation fee is represented by constant 120.d) The monthly charge is represented by coefficient 75.What is linear equation ?
Linear equation is the equation in which the highest power of the unknown variable is one. Linear equation are used to model the real life problem in the mathematical expressions.
The linear equation with dependent variable y and independent variable x can be written as,
[tex]y=mx+c[/tex]
Here, [tex]m[/tex] is the slope of the equation and [tex]c[/tex] is the y intercept.
Given information-
The total cost is modeled by the equation
[tex]y=120+75x[/tex]
In the above equation the, variable y is dependent variable and the variable x is independent variable. The constant term 120 is fixed.
a) The total cost is represented by-As the total cost is the overall cost of the dish television. This is shown by the dependent variable y, which given the final value of cost. Thus the total cost is represented by variable y.b) The number of months is represented by-The independent variable x represent the number of months.c) The installation fee is- As the one time installation fee is fixed which does not vary. Thus the constant 120 represent the installation fee.d) The monthly charge is-The monthly charge is written with independent variable y. Thus,The monthly charge is represented by coefficient 75.Hence,
a) The total cost is represented by variable y.b) The number of months is represented by is represented by variable x.c) The installation fee is represented by constant 120.d) The monthly charge is represented by coefficient 75.Learn more about the linear equation here;
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Use the graph to determine the functions type of zeros.
The quadratic function has zeros at x = -2, x = 0 (with multiplicity 2), x = 2, and x = 6. The zeros include simple roots and a double root, determined by the graph's behavior at the x-intercepts.
To determine the type of zeros for a quadratic function based on its graph, we need to consider the behavior of the parabola at the x-intercepts (zeros). The given points where the graph intersects the x-axis are (-2, 0), (0, 0), (2, 0), and (6, 0).
1. **Multiplicity of Zeros:**
- For the point (0, 0), the zero has multiplicity 2 since the graph touches the x-axis but doesn't cross it.
- For the points (-2, 0), (2, 0), and (6, 0), the zeros have multiplicity 1 since the graph crosses the x-axis at these points.
2. **Type of Zeros:**
- For the zero at x = 0 (multiplicity 2), it is a double root or a repeated zero.
- For the zeros at x = -2, x = 2, and x = 6 (multiplicity 1), they are simple roots.
3. **Discriminant:**
- The discriminant of a quadratic equation \(ax^2 + bx + c = 0\) is given by \(b^2 - 4ac\).
- If the discriminant is positive, the quadratic equation has two distinct real roots (simple roots).
- If the discriminant is zero, the quadratic equation has one real root with multiplicity 2 (double root).
- If the discriminant is negative, the quadratic equation has two complex conjugate roots.
In this case, the fact that the parabola touches the x-axis at (0, 0) without crossing it indicates a double root at x = 0. The other zeros at (-2, 0), (2, 0), and (6, 0) are simple roots.
Therefore, the type of zeros for the given quadratic function is a mix of simple roots and a double root.
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A 20-foot support post leans against a wall, making a 70° angle with the ground. to the nearest tenth of a foot, how far up the wall will the support post reach
Trigonometry
[tex]Sin\frac{Opposite}{Hypotenuse} Cos\frac{Adjacent}{Hypotenuse} Tan\frac{Adjacent}{Opposite}[/tex]
[tex]S\frac{O}{H} C\frac{A}{H} T\frac{A}{O}[/tex]
You know the hypotenuse and you want to find the opposite therefore you use, sine.
[tex]Opposite = Sin(70) *{20}[/tex]
Opposite = 18.79385242
Opposite = 18.8 feet5x=-15x+3000 simplify step by step
The answer is 150 to this question
Is the sum of two rational number is 5/18 if one of the number is 1/8 find the other
Answer: 4/8
Step-by-step explanation:
Equation: 1/8+x=5/18
-1/8 -1/8
x=4/8
Double Check: 4/8+1/8=5/8
HELP WILL PICK BRAINLIEST!
Choose the correct domain for f(x) = ex -2
(-∞,∞)
(0,∞)
[0,∞)
(-∞,0)
Answer:
The function has no undefined points nor domain constraints, therefore the Domain is (-∞ < x < ∞). Since your answers don't match the real results, the interval notation is (-∞,∞)
Step-by-step explanation:
What is the value of x?
The little rectangle in the top right means the angle is a right angle which equals 90 degrees.
This also means all the other angles are also 90 degrees.
Solve for x:
2x+8 = 90
Subtract 8 from both sides:
2x = 82
Divide both sides by 2:
x = 82/2
x = 41
Answer:
x = 41
Step-by-step explanation:
Since they are vertical angles, 90 = 2x + 8.
Then isolate the variable by subtracting 8 from both sides.
So 2x = 82.
Then divide each side by 2 to get x = 41.
You have a 1-gallon paint can in the shape of a cylinder. One gallon is 231 cubic inches. The radius of the can is 3 inches. What is the approximate height of the paint can? Use 3.14 for pi.
Answer:
The approximate height of the paint can is 8.2 in
Step-by-step explanation:
we know that
The volume of the cylinder ( can of paint) is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]V=231\ in^{3}[/tex]
[tex]r=3\ in[/tex]
[tex]\pi=3.14[/tex]
Substitute the values and solve for h
231=(3.14)(3)^{2} h
h=231/(3.14*9)=8.2 in
Answer is :
8
For IM..
Which values of x would make a polynomial equal to zero if the factors of the polynomial wrre (x+6) and (x+9)?
Negative 6 and negative 9 would :)
Polynomials are mathematical expressions involving variables raised with non-negative integers, coefficients and constants. The value of the solution that will make the polynomial equal to zero is -6 and -9.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
The values of x that would make a polynomial equal to zero if the factors of the polynomial are (x+6) and (x+9) are -6 and -9.
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Can someone help me with the First question ?
Answer:
Step-by-step explanation:
#1.
228 ÷ 6 = 38 in
#2.
186 ÷ 3 = 62 ft
#3.
360 ÷ 8 = 45 yd
#4.
119 ÷ 7 = 17 ft
I hope I helped you.
Answer:
Perimeter is the total outside dimension.
To find the length of one side, divide the total perimeter by the number of sides.
1. 228 / 6 = 38 inches.
2. 186 / 3 = 62 feet.
3. 360 / 8 = 45 yards
4. 119 / 7 = 17 feet.
Use a graphing calculator, or another piece of technology, to find the zeros of the function f(x)=−2x3+5x2+1.
What are the approximate zeros to the nearest tenth?
There may be more than one correct answer. Select all correct answers.
x≈0.2
x≈−0.2
x≈−2.58
x≈1.7
x≈2.58
x≈−1.7
The answer is 2.58
See attached picture of graph with the solution:
The approximate zeros of the function f(x)=-2x^3+5x^2+1, to the nearest tenth, are x ≈ 0.2, x ≈ -2.58, and x ≈ 1.7.
Explanation:To find the zeros of the function f(x)=−2x3+5x2+1, one uses a graphing calculator or similar piece of technology. After entering this function and graphing it, you locate the points where the curve intersects the x-axis. These points are the function's zeros or roots, as the function equals zero at these x-values.
For the function given, the zeros are approximately x ≈ 0.2, x ≈ -2.58, and x ≈ 1.7 when rounded to the nearest tenth. These values represent the x-coordinates of the points where the graph of the function intersects the x-axis.
Please note that because we're rounding to the nearest tenth, the actual zero could slightly differ.
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Need help ASAP!!
A triangle has side lengths of 34 in., 20 in., and 47 in. Is the triangle acute, obtuse or right?
A. right
B. obtuse
C. acute
For the answer I got B. obtuse. Is it correct?
16. A triangle has side lengths of 1.2, 4.6 and 5. Determine if the triangles is Acute, Obtuse, or Right.
For the answer I got Acute. Is it correct?
17. Find the value of x.
Picture 1 is my work for number 11.
Picture 2 is my work for number 16.
Picture 3 is what I need to use to solve for x.
Answer:
1. B (obtuse)
2. Obtuse
3. 20.92
Step-by-step explanation:
1.
We need to use the converse of the pythagorean theorem to solve this problem. Given that c is the longest side of a triangle, and a and b are the other two sides. The triangle is right triangle if [tex]c^2=a^2 +b^2[/tex]
The triangle is acute triangle if [tex]c^2 < a^2 + b^2[/tex]
The triangle is obtuse triangle if [tex]c^2 > a^2 + b^2[/tex]
the longest side of this triangle is 47, so we check:
[tex]47^2=2209[/tex], and
[tex]34^2 + 20 ^2 =1556[/tex]
Hence, c^2 is GREATER than a^2 + b^2, so the triangle is obtuse.
2. Using the points we showed above, we can again summarize:
If [tex]c^2 = a^2 + b^2[/tex] -- Right Triangleif [tex]c^2 < a^2 + b^2[/tex] -- Acute Triangleif [tex]c^2 > a^2 + b^2[/tex] -- Obtuse TriangleThis triangle's c (longest side) is 5. Let's check:
5^2 = 25, and
[tex](1.2)^2 + (4.6) ^2=22.6[/tex]
Hence, c^2 is GREATER than a^2 +b^2, so the triangle is obtuse.
3.
The side opposite of the 90 degree angle is the "hypotenuse", that is x. The side opposite the 35 degree angle is "opposite" side.
The trigonometric ratio that related "opposite" side to "hypotenuse" side is SINE. So we can write:
[tex]Sin(35)=\frac{Opposite}{Hypotenuse}\\Sin(35)=\frac{12}{x}[/tex]
Now, cross multiplying and solving:
[tex]Sin(35)=\frac{12}{x}\\x*Sin(35)=12\\x=\frac{12}{Sin(35)}\\x=20.92[/tex]
The first triangle is obtuse since the square of the longest side is greater than the sum of the squares of the other sides. The second triangle is acute since the square of the longest side is less than the sum of the squares of the other sides. Both answers provided are correct.
Explanation:To determine the type of triangle (acute, obtuse, or right) based on the side lengths, you can apply the Pythagorean theorem. For the triangle with side lengths of 34 in., 20 in., and 47 in., you compare the square of the largest side (472) with the sum of the squares of the other two sides (342 + 202). If the square of the largest side is greater, the triangle is obtuse. Calculating gives us 2209 (472) and 1556 (342) + 400 (202), equaling 1956, thus 2209 > 1956 and the triangle is indeed obtuse. Your answer is correct.
For the second triangle with side lengths of 1.2, 4.6, and 5, we again apply the Pythagorean theorem. If the square of the largest side (52) is equal to the sum of the squares of the other two sides (1.22 + 4.62), the triangle is right. If it’s less, the triangle is acute.
Calculating gives us 25 (52) and 1.44 (1.22) + 21.16 (4.62), equaling 22.60, thus 25 > 22.60 and the triangle is acute. Your answer is correct.
If the Jonas family wanted to plant 3 bushes that needed to be 3 feet apart and 3 feet away from the fence around the yard, would they have room?
Answer:
Not enough info.
Step-by-step explanation:
Not enough information, how big is the fence perimeter wise? What is the shape of the fence? If the fence is square and 2,000 feet long, of course there's room. If its a square fence that's 2 feet long, there is no room at all.
please help me out...........
Answer:
N(c, b)Step-by-step explanation:
If N is midpoint between Q and R, then use the formula of a midpoint:
[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
We have the points Q(0, 2b) and R(2c, 0). Substitute:
[tex]x=\dfrac{0+2c}{2}=\dfrac{2c}{2}=c\\\\y=\dfrac{2b+0}{2}=\dfrac{2b}{2}=b[/tex]
Identify the circumference of ⊙S in which A=64π ft^2. HELP ASAP!!
C = 24π ft
C = 32π ft
C = 16π ft
C = 8π ft
Answer:
C = 16π ft
Step-by-step explanation:
If we know the area
A = pi r^2
64 pi = pi r^2
Divide each side by pi
64 = r^2
Take the square root of each side
8 = r
The radius is 8
Now we can find the circumference
C = 2 *pi*r
C = 2*pi*8
C = 16pi
Answer:
[tex]\large\boxed{C=16\pi\ ft^2}[/tex]
Step-by-step explanation:
The formula of an area of a circle:
[tex]A_O=\pi r^2[/tex]
r - radius
We have
[tex]A_O=64\pi\ ft^2[/tex]
Substitute:
[tex]\pi r^2=64\pi[/tex] divide both sides by π
[tex]r^2=64\to r=\sqrt{64}\\\\r=8\ ft[/tex]
The formula of a circumference:
[tex]C=2\pi r[/tex]
Substitute:
[tex]C=2\pi(8)=16\pi\ ft[/tex]
25 POINTS ANS BRAINLIEST
The two dot plots below compare the forearm lengths of two groups of schoolchildren:
Based on visual inspection of the dot plots, which group appears to have the longest average forearm length?
Group A, because seven children have a forearm length longer than 10 inches
Group B, because two children have a forearm length longer than 10 inches
Group A, because one child in the group has the least forearm length of 9 inches
Group B, because three children in the group have the least forearm length of 9 inches
Answer: it is a
Step-by-step explanation:
It is a because if you add them all together you will see that be is less so you can cross does out so you are left with a or c. C is not the correct ans because none of the kids had a forearm less than 9. And all seven of the kids had a forearm more than 10 inches.
Darren kept track of the number of e-mails he received from one of his customers each day for 14 days on the dot plot. Which statement must be true according to the dot plot?
The data is skewed left and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.
The data is skewed left and shows that on half of the days, Darren received 7 to 9 e-mails from the customer.
The data is skewed right and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.
The data is skewed right and shows that on half of the days, Darren received 7 to 9 e-mails from the customer.
Answer: A. The data is skewed left and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.
Step-by-step explanation: Most of the Data is on the right so it is skewed left, and most of the emails are on 11 and 12 so that is why A is correct.
Given that tan theta = square root of 3 over 4, and 0 < theta < pi over 2, what is the exact value of cot theta?
Answer:
[tex]\frac{4\sqrt{3} }{3}[/tex]
Step-by-step explanation:
4sqrt3/3
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 13 subjects had a mean wake time of 102.0 min. After treatment, the 13 subjects had a mean wake time of 79.4 min and a standard deviation of 21.2 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a 90% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 102.0 min before the treatment? Does the drug appear to be effective?
Answer:
Confidence interval: 11.5 < µ < 30.9
Read below to see conclusion:
Step-by-step explanation:
n = 13, x = 79.4, s = 21.2, Z = 1.645 (z score for a confidence interval with 90% confidence)
Use the formula to find the error: E = Z(s/√n)
We have: E = 1.645(21.2/√13) = 9.7
Now construct the confidence interval:
x - E < µ < x + E
21.2 - 9.7 < µ < 21.2 + 9.7
11.5 < µ < 30.9
Yes, the drug appears to be effective because the estimated wake time for a population using this drug will be between 11.5 and 30.9 minutes. The upper end of this interval is much lower than 102, so it appears as though the drug is effective.
Identify the graph of 4x^2+5y^2=20 for T(5,-6) and write an equation of the translated or rotated graph in general form..
Answer:
The answer is ellipse of equation 4x² + 5y² - 40x + 60y + 260 = 0 ⇒ answer (b)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
* 4x² + 5y² = 20
∵ A = 4 , B = 0 , C = 5
∴ B² - 4 AC = (0)² - 4(4)(5) = -80
∴ B² - 4AC < 0
∴ The graph is ellipse or circle
* If A and C are nonzero, have the same sign, and are not
equal to each other, then the graph is an ellipse.
* If A and C are equal and nonzero and have the same
sign, then the graph is a circle.
∵ A and C have same signs with different values
∴ It is an ellipse
* Now lets study T(5 , -6), that means the graph will translate
5 units to the right and 6 units down
∴ x will be (x - 5) and y will be (y - -6) = (y + 6)
* Lets substitute the x by ( x - 5) and y by (y + 6) in the equation
∴ 4(x - 5)² + 5(y + 6)² = 20
* Use the foil method
∴ 4(x² - 10x + 25) + 5(y² + 12y + 36) = 20
* Open the brackets
∴ 4x² - 40x + 100 + 5y² + 60y + 180 = 20
* Collect the like terms
∴ 4x² + 5y² - 40x + 60y + 280 = 20
∴ 4x² + 5y² - 40x + 60y + 280 - 20 = 0
∴ 4x² + 5y² - 40x + 60y + 260 = 0
* The answer is ellipse of equation 4x² + 5y² - 40x + 60y + 260 = 0
Answer:
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Step-by-step explanation:
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Select the first correct reason why the given series converges.
a. convergent geometric series
b. convergent p-series
c. integral test
d. comparison with a convergent p-series
e. converges by limit comparison test f. converges by alternating series test e 1. ∑n=2∞n2+n‾√n4−4 f 2. ∑n=1∞n2+ln(n)n2−9n f 3. ∑n=1∞(cos(nπ))ln(6n) f 4. ∑n=1∞(−1)n7n+5 f 5. ∑n=1∞(−1)nn‾√n+4 c 6. ∑n=2∞4n(ln(n))2
Answer:
E. Converges by limit comparison test.
Step-by-step explanation:
Here is something that might help you on this
https://study.com/academy/answer/select-the-first-correct-reason-why-the-given-series-converges-displaystyle-sum-n-1-infty-1-n-frac-sqrt-n-n-2-a-convergent-geometric-series-b-convergent-p-series-c-comparison-or-limi.html.
This question involves the application of different series convergence tests in calculus. The first correct reasons why the given series converged were identified using the comparison to a convergent p-series, integral test, and the alternating series test.
Explanation:This question relates to the convergence of series in calculus. In order to determine why a given series converges, we need to apply various convergence tests. Here are the first correct reasons why the provided series converge:
∑n=2∞n2+n/√n4−4 converges by comparison with a convergent p-series.∑n=1∞n2+ln(n)/n2−9n converges by the integral test.∑n=1∞(cos(nπ))ln(6n) converges by the alternating series test.∑n=1∞(−1)n/7n+5 converges by the alternating series test.∑n=1∞(−1)n/√n+4 converges by the alternating series test.∑n=2∞4n(ln(n))2 converges by the integral test.Learn more about Convergence of Series here:https://brainly.com/question/33953891
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1. The fabric Josef is using comes in 100 square-inch pieces that cost $6.25 each. What will his fabric cost? Show your work.
2. a student made a toy chest for his baby sister's square building blocks. Six layers of blocks can fit in the box, and each layer has 15 blocks. How many building blocks can the toy chest hold? show your work.
PLEASE HELP
Answer:
The asnwers for your two question problem are
1. $625
2. 90 building blocks
Step-by-step explanation:
First problem
The fabric Josef is using comes in 100 square-inch pieces that cost $6.25 each. What will his fabric cost?
* The fabric has 100 pieces
* Each piece costs $6.25
Total amount for the fabric = $6.25*100 = $625
Second problem
A student made a toy chest for his baby sister's square building blocks. Six layers of blocks can fit in the box, and each layer has 15 blocks. How many building blocks can the toy chest hold?
* 6 layers of blocks fit in the box
* Each layer has 15 blocks
Total amount of blocks = 6*15 blocks = 90 blocks
2)Explain how the letter x is used when writing expressions, and give an example.
Answer:
x + y = z
y=5
z=10
x = z - y =10-5 =5
Step-by-step explanation: